Combinations and multiplications of foldable modules and their modifications

ABSTRACT

An article or portion of an article comprising a combination of at least two foldable modules that mutually hinder either their folding or unfolding during normal operation until additional force is applied on particular spots along the mutual foldable edges that connect the modules. The article or the portion of the article not only can perform almost as well as non-folding equivalents but also can have the advantages that foldability offers. Such foldable modules can define not only tubular cylindrical shapes but also conical ones and mixtures between them. They can also be built as closing collapsible modules.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional Patent Application No. 62/500,534 (filed on May 3, 2017).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows examples of cylindrical and conical combinations of foldable modules/sections.

FIG. 2 shows a very simple and very symmetrical type of foldable module composed of four identical isosceles right-angled triangles.

FIG. 3 depicts a simple collapsible unit made of four identical non-isosceles right-angled triangles.

FIG. 4 shows a foldable cylindrical module composed of sets of two right-angled triangles and two trapezoids.

FIG. 5 depicts a foldable cylindrical module composed of four trapezoids.

FIG. 6 shows general and/or asymmetric combinations and multiplications of foldable cylindrical units composed of four triangles.

FIG. 7 depicts general and/or more asymmetric constructions of foldable cylindrical modules and their combinations composed of four quadrilaterals or mixture between quadrilaterals and triangles.

FIG. 8 demonstrates foldable combinations of modules built by mirroring modules depicted in FIG. 2 and FIG. 3.

FIG. 9 shows foldable combinations of modules built by mirroring modules depicted in FIG. 4.

FIG. 10 shows foldable combinations of modules built by mirroring modules depicted in FIG. 5.

FIG. 11 demonstrates a simple and symmetrical module and its combination/multiplication composed of isosceles triangles.

FIG. 12 demonstrates a simple module and its combination/multiplication composed of non-isosceles triangles.

FIG. 13 depicts a conical module and its combination/multiplication composed of triangles and trapezoids.

FIG. 14 depicts a conical module and its combination/multiplication composed of triangles and trapezoids.

FIG. 15 depicts a conical module and its combination/multiplication composed of trapezoids.

FIG. 16 shows general and/or asymmetric combinations and multiplications of foldable conical units composed of four triangles.

FIG. 17 depicts general and/or more asymmetric constructions of foldable conical modules and their combinations composed of four quadrilaterals or mixture between quadrilaterals and triangles.

FIG. 18 depicts a practical way to build a rolled version from an unrolled one and vice-versa of any cylindrical or conical foldable modules and their combinations.

FIG. 19 demonstrates the need of correction of outer edges when mixing foldable modules defining different surfaces.

FIG. 20 shows trimming and mirroring of cylindrical or conical foldable modules and/or combinations between such modules.

FIG. 21 shows trimming and mirroring of cylindrical or conical foldable modules and/or combinations between such modules.

FIG. 22 shows trimming and mirroring of extended cylindrical or conical foldable modules and/or combinations between such modules.

FIG. 23 depicts a very simple round collapsible closing module appropriate for cylindrical surfaces.

FIG. 24 depicts a very simple round collapsible closing module appropriate for conical surfaces.

FIG. 25 depicts a very simple round collapsible closing module appropriate for conical surfaces.

FIG. 26 shows an asymmetrical closing module for cylindrical or conical surfaces.

FIG. 27 shows a trimmed round collapsible closing module appropriate for cylindrical surfaces.

FIG. 28 demonstrates a trimmed round collapsible closing module appropriate for conical surfaces.

FIG. 29 demonstrates a trimmed round collapsible closing module appropriate for conical surfaces.

FIG. 30 depicts a very simple flat collapsible closing module appropriate for cylindrical surfaces.

FIG. 31 depicts a very simple flat collapsible closing module appropriate for conical surfaces.

FIG. 32 depicts a very simple flat collapsible closing module appropriate for conical surfaces.

FIG. 33 shows a trimmed flat collapsible closing module appropriate for cylindrical surfaces.

FIG. 34 shows a trimmed flat collapsible closing module appropriate for conical surfaces.

FIG. 35 shows a trimmed flat collapsible closing module appropriate for conical surfaces.

FIG. 36 depicts a very simple filleted flat collapsible closing module appropriate for cylindrical surfaces.

FIG. 37 depicts a trimmed and filleted flat collapsible closing module appropriate for cylindrical surfaces.

FIG. 38 depicts a very simple filleted flat collapsible closing module appropriate for conical surfaces.

FIG. 39 depicts a very simple filleted flat collapsible closing module appropriate for conical surfaces.

FIG. 40 depicts a trimmed and filleted flat collapsible closing module appropriate for conical surfaces.

FIG. 41 depicts a trimmed and filleted flat collapsible closing module appropriate for conical surfaces.

FIG. 42 shows a sharp collapsible closing module appropriate for cylindrical or conical surfaces.

FIG. 43 shows a trimmed sharp collapsible closing module appropriate for cylindrical or conical surfaces.

FIG. 44 depicts mirroring of closing modules appropriate for cylindrical surfaces.

FIG. 45 depicts trimming and mirroring of closing modules.

FIG. 46 depicts trimming and mirroring of closing modules.

FIG. 47 depicts combining trimmed and mirrored closing modules with tubular foldable surfaces.

FIG. 48 depicts mirroring of flat closing modules.

FIG. 49 depicts face removal and mirroring of flat closing modules.

FIG. 50 shows combining of mirrored flat closing modules with tubular foldable modules.

FIG. 51 shows combining of different closing modules.

FIG. 52 demonstrates merging of round and sharp cylindrical and conical closing modules with appropriate cylindrical and conical tubular modules.

FIG. 53 demonstrates merging of round and sharp cylindrical and conical closing modules with appropriate cylindrical and conical tubular modules with removed intersecting edges on the tubular surface.

FIG. 54 depicts extension or removal of faces.

FIG. 55 shows shape stretching of symmetrical tubular and closing modules and their symmetrical combinations.

FIG. 56 depicts simple cylindrical and conical modules composed of two faces.

FIG. 57 demonstrates foldable junctions between two or more tubular structures.

FIG. 58 shows flattening and merging of outer edges of tubular structures.

FIG. 59 shows flattening of outer edges of tubular structures.

FIG. 60 demonstrates closing of flattened outer edges of tubular structures.

FIG. 61 demonstrates closing of flattened outer edges of tubular structures.

FIG. 62 shows thicker shell modifications of foldable modules.

FIG. 63 shows a thicker shell modification of foldable modules.

FIG. 64 depicts a rigid material modification of foldable modules.

FIG. 65 shows partly folded states of structures composed of foldable modules.

FIG. 66 demonstrates possible geometry of folding edges/hinges.

FIG. 67 depicts modified foldable modules that fill cavities in the folded structure.

FIG. 68 depicts modified foldable modules that fill cavities in the folded structure.

FIG. 69 depicts a collapsible container composed of foldable modules.

FIG. 70 depicts a collapsible container composed of foldable modules.

FIG. 71 depicts a collapsible container composed of foldable modules.

FIG. 72 depicts a collapsible container composed of foldable modules.

FIG. 73 depicts a collapsible container composed of foldable modules.

FIG. 74 depicts a collapsible container composed of foldable modules.

FIG. 75 depicts a collapsible container composed of foldable modules.

FIG. 76 depicts a collapsible container composed of foldable modules.

FIG. 77 depicts a collapsible container composed of foldable modules.

FIG. 78 depicts a collapsible container composed of foldable modules.

FIG. 79 shows a collapsible pipe structure composed of foldable modules.

FIG. 80 shows a collapsible pipe structure composed of foldable modules.

DETAILED DESCRIPTION

I have invented combinations and multiplications of foldable modules and their modifications that can be used for articles or portions of articles as collapsible shell structures.

The main problems of the currently known foldable shell structures used for collapsible articles are that they are not very stable in unfolded position, they require to be made of very soft materials, they can not provide a smooth cylindrical or conical surface.

The advantages of the structures composed of the described collapsible modules/sections are:

-   -   They are self supporting and very stable in unfolded position     -   They can form smooth and round surfaces     -   They can be made of variety of different materials including         more rigid ones     -   They can be produced by different methods and technologies     -   They can be very compact in folded position     -   They can be composed of both cylindrical and/or conical surfaces     -   They can operate also in partly folded states, giving         variability in shape and size

Tubular structures composed by combining and multiplying two or more foldable modules/sections and their modifications described in this specification keep their round shape naturally in unfolded position and are almost as stable as non-folding tubular structures when axially compressed until additional force is applied on particular spots along the mutual foldable edges that connect the modules/sections. The folding process involves an abrupt transition between unfolded (round-shaped) and semi folded (flat-shaped) states giving different behaviour of the structure in the two states. In the flat-shaped state these structures usually behave like springs. On the contrary, in unfolded position they behave like regular non-folding equivalents.

The abovementioned qualities give the option of taking advantage of foldability without compromising with the stability and the general performance of articles composed of such foldable sections. Moreover, even harder and non-rubber-like materials can be used reducing the thickness and the weight of the described foldable structures.

Examples of cylindrical and conical combinations of foldable modules/sections described below are shown in FIG. 1. The cylindrical example demonstrates that the tubular portion of such collapsible structures can contain different types of foldable sections.

An extremely simple and symmetrical type of foldable modules is shown in FIG. 2. It is composed of four identical isosceles right-angled triangles and folds in a square shape. The edges coinciding the hypotenuses 101, 102, 103, and 104 of the triangles form valley creases during folding when combined with other collapsible modules. The edges that coincide with the catheti 105, 106, 107, 108, and 109 (the internal edges) form mountain creases during folding. Foldable tessellations based on this collapsible unit are similar to the so called Yoshimura pattern that describes the behaviour of buckling of thin cylindrical shell structures. The big difference is that the number of triangles in the looped strip they are composed of are reduced to four. This reduction brings the qualities explained in the previous paragraph, because in general, it is not the natural way a thin cylindrical shell collapses when exposed only to axial pressure. It requires extra force to be applied on the edges that form valley creases during folding in order to start the collapsing process. To unfold a structure composed of this type of folding modules it can be axially pulled or force can be applied on any two opposing convex vertices in unfolded or semi-folded state.

Another simple collapsible unit can be made of four identical non-isosceles right-angled triangles 110, 111, 112, 113 shown with bold continuous lines in FIG. 3. In this case it folds in a rectangular shape. It can be multiplied and combined with itself represented by triangles 114, 115, 116, 117 shown with thin continuous lines, with a mirrored version of itself represented by triangles 118, 119, 120, 121 shown with thin dashed lines, or it can be combined with a different set of identical right-angled triangles, including the one in FIG. 2.

The foldable units shown in FIG. 2 and FIG. 3 can be modified by trimming them in rolled/looped state with a plane 122 that is perpendicular to the axis of the cylinders they form giving sets of two right-angled triangles and two trapezoids FIG. 4. The same result can be achieved by cutting the unrolled module by a straight line 123 parallel to the hypotenuses. By trimming these units with one more different plane 124 or line 125 of this type a foldable unit composed of two pairs of trapezoids can be achieved FIG. 5. The two types of trapezoids can be identical or they can be different, depending on the place of the two cutting planes/lines. If the four trapezoids are isosceles the tessellations that this module can form are similar to the so called “chicken wire tessellation”. The main difference again is that the number of trapezoids in the looped strip are reduced to just four, keeping the round shape of the tube naturally in unfolded position when combined with another appropriate foldable strip. The edges that coincide with the big bases of the trapezoids 126, 127, 128, and 129 form valley creases during folding when combined with other collapsible modules. On the contrary, the edges coinciding with the small bases of the trapezoids 130, 131, 132, and 133 form mountain creases when combined with other collapsible modules. These are the edges/hinges 130, 131, 132, and 133 that can be pressed to unfold the structure. Combinations composed of such modules experience less deformation of the material during folding and unfolding compared to the modules composed of triangles which makes them more appropriate when stiffer materials are used.

It is important to be known that trimmed sides of modules depicted in FIG. 3 can not be combined with cut modifications of modules depicted in FIG. 2 because their outer looped edges (in rolled state) do not coincide in folded position. They form a parallelograms in the first case and rectangles in the second. Trimmed modules of the type shown in FIG. 3 can not combine with themselves but they can be combined with mirrored versions of themselves.

More general and/or asymmetric combinations and multiplications of foldable units composed of four triangles that are not necessarily right-angled can be built (FIG. 6). The general rule in this case is that every angle in any of the four triangles that is between two angles from other two triangles must equal the sum of these two angles. The dependences of this type in FIG. 6 are: α2=α4+α12; α5=α3+α7; α8=α6+α10; α11=α1+α9 for the basic module shown in bold continuous lines in the upper drawing depicting an example in an unrolled state. Following the same rule the dependences between the angles in an appropriate module for combination shown with thin continuous lines are: α13=α16+α24; α17=α15+α20; α19=α18+α22; α23=α14+α21. Another important dependence is that the corresponding edges overlapping in rolled position 134 and 135, 136 and 137 or in folded position 138 and 139, 140 and 141, 142 and 143 have equal lengths. The edges coinciding in rolled/looped position 134 and 135, 136 and 137 are parallel. The geodesic lines 144, 145, and 146 connecting the vertices which overlap in rolled/looped position all have equal lengths, they are parallel when unrolled and are shown with thin dashed lines in the same upper drawing in FIG. 6.

The foldable modules depicted in FIG. 2 and FIG. 3 can be considered as special cases of this general geometric construction.

General and/or more asymmetric constructions of foldable modules and their combinations composed of four quadrilaterals or mixture between quadrilaterals and triangles are also possible (FIG. 7). They can be built by trimming one set of four triangles that satisfy the dependences in FIG. 6 by one or two nonintersecting polylines. Every endpoint of every line segment of such a polyline must lie on an edge/hinge that is common for two of the four triangles (an internal edge in rolled state). It can also coincide with an intersection of two edges/hinges of this type leaving a triangle not cut. A line segment of such polylines can not overlap these edges/hinges but they can overlap the outer looped (in rolled state) edges leaving a triangle not trimmed again.

The geodesic lines that connect the two endpoints of the whole polyline 147 and 148 are parallel to the geodesic lines connecting the vertices of the triangles which overlap in rolled position 149 and 150, they also have the same length and are shown with thin dashed lines in the upper two drawings in FIG. 7. The lengths of the corresponding segments that overlap in rolled state 151 and 152, 153 and 154, 155 and 156 are equal.

Using the endpoints of the segments of the polyline a new set of triangles satisfying the rules in FIG. 6 can be build. The geodesic lines that connect the two endpoints of the whole polyline 157 and 158 are again parallel to the geodesic lines connecting the vertices of the triangles which overlap in rolled position 159 and 160, they again have the same length. The lengths of the corresponding segments that overlap in rolled state 161 and 162, 163 and 164, 165 and 166 are again equal.

The internal edges/creases must not only go through the endpoints of the segments of the polyline, but also follow the rule of foldability of patterns composed of vertices incident to four edges—the sum of opposite sector angles equals 180°. This rule can be used when an endpoint along the polyline does not coincide with a vertex of any of the auxiliary (in this case) triangles. In FIG. 7 the dependences are: β3+β5=β4+β6=β7+β9=β8+β10=β11+β13=β12+β14=β15+β2=β16++β1=180°.

The foldable modules described in FIG. 4 and FIG. 5 can be considered as special cases of this general geometric construction. Even the general construction in FIG. 6 can be considered as a special case of one following the rules from FIG. 7 if the cutting polylines coincide and overlap the outer looped (in rolled state) edges of the triangles in the set. And vice-versa, the construction in FIG. 7 can be considered as a combination of modified/trimmed versions of foldable modules composed of four triangles.

The simple foldable modules depicted in FIG. 2 and FIG. 3 can form foldable combinations by mirroring them FIG. 8. This is valid also for their cut modifications depicted in FIG. 4 and FIG. 5. This is demonstrated in FIG. 9 and FIG. 10.

Foldable asymmetrical tubular modules composed of triangles, by a mixture of triangles and quadrilaterals, or only of quadrilaterals can also be modified by trimming them by planes perpendicular to their longitudinal axis and than mirrored. The planes must intersect all four internal edges/hinges in a foldable module.

Not only cylindrical but also conical foldable modules composed of four polygons are possible.

A simple and symmetrical one is shown in FIG. 11. It is composed of two pairs of isosceles triangles and is similar to the cylindrical foldable unit shown in FIG. 2. The main difference is that the 45° angles are decreased in one of the pairs 169 and 170 and respectively increased with the same degree in the other pair of triangles 167 and 168. Angle α25=45°+Δ1 and angle α26=45°−Δ1. It folds in rhomboidal shape. This type of foldable module can be combined with a scaled version of itself where triangles 173 and 174 are similar to 167 and 168 and triangles 171 and 172 are similar to 169 and 170. These types of foldable patterns can also be combined with the next type of foldable module described below.

The simple foldable conical module presented in FIG. 12 is similar to the cylindrical one shown in FIG. 3. The main difference is that the 90° angles are increased in pairs 175 and 176 in the first module and 179 and 180 in the second module and respectively decreased with the same degree in pairs 177 and 178 in the first module and 181 and 182 in the second module. Angle α27=90°+Δ2 and angle α28=90°−Δ2. Such modules fold in parallelograms. All of the vertices of the four triangles in a module lie on concentric arcs 183, 184, 185 when unrolled, their center is the apex of the unrolled conical surface.

Foldable modifications can be built by trimming the four triangles in the conical constructions shown in FIG. 11 and FIG. 12 by polylines 186, 192 composed of segments parallel to the outer edges, looped in rolled state (FIG. 13 and FIG. 14). The endpoints of the segments must lie on the edges/hinges that are common for two corresponding triangles from the same set (the internal edges/hinges) 187, 188, 189, 190, 191 and 193, 194, 195, 196, 197. Similar to the cylindrical equivalents, the trimmed modules in FIG. 12 can not combine with trimmed and scaled versions of themselves and with the ones from FIG. 11 but they can combine with constructions that satisfy the rule of foldability of patterns composed of vertices incident to four edges explained in FIG. 7—the sum of opposite sector angles equals 180°.

Modules composed of four trapezoids are also possible if the triangles are cut by two different polylines 198, 199 (FIG. 15).

More general foldable conical constructions composed of four triangles can be built (FIG. 16). They are similar to the cylindrical ones (FIG. 6). The main difference is that the edges/hinges that coincide in rolled position 200 and 201, 202 and 203 are not parallel in the unrolled one. They are rotated relative to one another around the apex of the unrolled conical surface. Their endpoints lie on concentric arcs 204, 205, 206 with centers the apex too. The dependences between the angles follow the same rule: α30=α32+α39; α34=α31+α35; α36=α33+α38; α40=α37+α29 for the initial module shown with bold continuous lines and α41=α44+α52; α45=α43+α48; α47=α46+α50; α51=α42+α49 for the appropriate foldable set of four triangles it is combined with. Edges that overlap in folded position have equal lengths. The constructions in FIG. 11 and FIG. 12 can be considered as special cases of this general construction.

More general constructions and combinations of foldable conical modules composed of quadrilaterals or mixture between quadrilaterals and triangles, similar to the cylindrical ones depicted in FIG. 7, are possible too (FIG. 17). They can be built following the same procedures. An initial foldable module composed of four triangles following the rules in FIG. 16 is then cut by one or two non-intersecting polylines. The endpoints of the sectors of the polylines must lie on the internal edges/hinges in the set 207, 208, 209, 210, 211. They can also coincide with the intersection of two edges leaving a triangle not cut. The two endpoints of the whole polyline must lie on an arc with center the apex of the unrolled conical surface. Using the endpoints of the sectors of the initial polyline a new set of four foldable triangles can be built where the internal edges/hinges of the new set 216, 217, 218, 219, 220 must go through the endpoints of the initial poliline and the general rule of foldability of patterns composed of vertices incident to four edges can be used again—the sum of opposite sector angles equals 180°. In this case the equations are: β17+β32=β18+β31=β19+β21=β20+β22=β23+β25=β24+β26=β27+β29=β28+β30=180°, The foldable modules in FIG. 18, FIG. 14, and FIG. 15 can be considered as special cases of this general construction.

The general construction in FIG. 16 can also be considered as a special case of the one in FIG. 17 if the cutting polylines coincide and overlap the outer looped (in rolled state) edges of the triangles in the particular set 212, 213, 214, 215 and 221, 222, 223, 224. And vice-versa, the construction in FIG. 17 can be considered as a combination of modified/trimmed versions of foldable conical modules composed of four triangles. Moreover, cylindrical foldable modules can be considered as spacial cases of their conical modifications with apexes at infinity. This way all conical and cylindrical modules described can be considered as special cases of the construction shown in FIG. 17 or as modifications of the one depicted in FIG. 16.

Mirrored versions of the general cylindrical and conical modules are also foldable. Rolling the tessellations in opposite direction will also result in mirrored versions.

A practical way to build a rolled version from an unrolled one and vice-versa of any of the described cylindrical or conical foldable modules and their combinations is by drawing a net of lines and finding the corresponding points of intersection between them and the edges/hinges (FIG. 18). Straight lines in unrolled state appear as geodesic ones in the rolled state and vice-versa.

When two modules with different surfaces are combined the shape of the corresponding edges must be corrected. When the new common edge/hinge is a mountain one 225 the two surfaces must be extended equally. On the contrary, if it is a valley one 226 they must be contracted equally (FIG. 19).

Every cylindrical or conical foldable module described above can be trimmed and mirrored by a free plane 227, 228, 229, 236, 237 intersecting all of its four internal edges/hinges in a foldable module 230, 231, 232, 233, 234, 235, 238, 239, 240, 241 giving new foldable combinations (FIG. 20 and FIG. 21). The plane can be inclined with respect to only one of the planes of symmetry, as shown in the examples, or it can be a random plane intersecting all of the internal edges/hinges. If needed, a surface 242 can be extended first 243 and then trimmed and mirrored (FIG. 22). The cutting plane can also go through the endpoints of the internal edges/hinges 244, 245.

Several types of closing foldable units can be combined with the described cylindrical and conical modules and their modifications.

A round and simple module is shown in FIG. 23. It can be built as an intersection of the modules in FIG. 2 or FIG. 3 with an identical longitudinally halved cylindrical surface 246 with an axis going through the midpoints of the hypotenuses of the rolled right-angled triangles 247. It can also be built by drawing a parallel net of pairing lines 248 and 252, 249 and 253, 250 and 254, 251 and 255 having equal lengths that overlap in folded position as shown in the upper drawings of FIG. 23.

With some approximation the pairing line strategy can be used to build closing foldable modules for conical surfaces (FIG. 24 and FIG. 25).

More asymmetrical closing units for tubular surfaces can also be built (FIG. 26). In this case the lengths of the line segments lying on the closing surface equal the sum of the lengths of the corresponding segments lying on the looped tubular surface or its close approximation. If the cross section of the tubular surface they close is not symmetrical this type of closing module will also be more asymmetrical than the example in FIG. 26.

The foldable closing units explained above can be trimmed and combined with trimmed cylindrical and conical modules (FIG. 27, FIG. 28, FIG. 29). The general rule is that the corresponding outer edges of the two modules that are combined must have equal lengths and same shapes in folded and unfolded position.

Flat rectangular closing modules are also possible (FIG. 30, FIG. 31, FIG. 32). The equality of angles in FIG. 31 and FIG. 32 is shown with α53 and α54. The examples shown are for square flat closing surfaces but keeping the angle dependencies nonsquare rectangular units can be built.

Trimmed modifications of the flat closing modules are possible too (FIG. 33, FIG. 34, FIG. 35). The equality of angles in FIG. 34 and FIG. 35 is shown with α55 and α56.

The flat modules can also be filleted in order to be smoother (FIG. 36, FIG. 37, FIG. 38, FIG. 39, FIG. 40, FIG. 41).

Sharp foldable closing modules for cylindrical and conical modules can be built (FIG. 42 and FIG. 43). They can be constructed using the same auxiliary pairing lines that can be used to build a round closing module for the continuation of the same cylindrical or conical looped surface 256, 257.

Every closing module for cylindrical surfaces described can be mirrored in a foldable structure FIG. 44.

Cylindrical and conical closing units can also be cut and mirrored by planes FIG. 45, FIG. 46, FIG. 47. These planes can be perpendicular to the planes of symmetry or they can be inclined.

The flat closing modules can be mirrored by a plane that coincides with the flat portion 258 of the closing surface FIG. 48. The flat face can be removed fully or partly if needed FIG. 49. They can be combined with tubular surfaces, cylindrical or conical, depending on the type of the flat closing modules FIG. 50.

Different closing modules or their trimmed modifications can be combined and form foldable structures FIG. 51. The general rule again is that the corresponding outer edges of the two modules that are combined must have equal lengths and same shapes in folded and unfolded position.

Round and sharp cylindrical and conical closing modules and their cut modifications can be merged with their corresponding cylindrical and conical tubular modules FIG. 52 and FIG. 53.

Combinations of two or more foldable modules can be modified by removing partly or fully faces or by extending them without making the whole structure unstable and without interfering with the folding process (FIG. 54). Such faces can be part of both tubular and closing modules.

This shape of all symmetrical tubular and closing modules and their symmetrical combinations can be stretched as shown in FIG. 55. If they have two planes of symmetry they can be stretched both directions.

Both, tubular and closing modules, can be combined with a simple type of tubular foldable units as shown in FIG. 56.

A simple folding module from FIG. 56 can be combined with the sharp cylindrical and conical foldable closing modules depicted in FIG. 42 and FIG. 43 and form foldable junctions between two or more tubular structures (FIG. 57). The closing face of the sharp module can be removed fully or partly and the corresponding portion of the surface of the simple module can also be removed fully or partly in order to connect the spaces inside the tubes.

Combinations of cylindrical and/or conical tubular modules can be modified by flattening the outer edges 259, 260, 261, 262, 263 as shown in FIG. 58, FIG. 59, FIG. 61.

If the end modules/sections are cut they can be closed fully or partly with additional faces 264, 265 as shown in FIG. 60 and FIG. 61.

The shell of the folding modules can be thicker if the material allows enough flexibility (FIG. 62 and FIG. 63).

Using rigid materials is also possible in combinations of two tubular modules if the thick sections are oriented in a way that they do not block the bending of the shell FIG. 64. Additional transverse division of the thick sections or living hinge patterns can also be used to provide bending capabilities to a rigid shell.

Structures composed of cylindrical and conical collapsible modules can function in partly folded states (FIG. 65) giving either symmetrical or asymmetrical solutions. This also can provide interactivity to the articles they are used for by giving the option to sculpture them.

Examples of possible geometry of the folding edges/hinges are shown in FIG. 66. They can be achieved by either making the edges more flexible than the surface material or by making them stiffer than it but flexible enough at the zones of intersection.

The edges/hinges can be made of the same material as the surface or they can be made of a different one. If the materials used for the edges/hinges have enough elasticity and the materials used for the surface offer enough flexibility structures composed of combinations of the foldable modules disclosed can also be self deployable or self-folding depending on which is the natural state of its elements.

The edges/hinges can be continuous or broken into sections leaving bridges connecting the surface elements. The flexibility of the edges/hinges can also be achieved by making sequences of wholes along them. Some edges can even be fully cut to serve as openings when appropriate.

The geometry of the edges or their sections that do not serve as hinges can be modified if the achieved modification does not interfere undesirably with the folding process. Openings can be placed on the surface elements and even over the edges/hinges.

The shape of the surface elements can be modified in order to follow the shape of another element in folded position, for example, when in folded position a container is needed to be completely empty (FIG. 67 and FIG. 68).

Combinations of foldable modules can be made of one material or by multiple materials for the different modules or parts of them.

Examples of possible material options for the modules or parts of them can be: plastic, rubber, silicone, paper, cardboard, leather, fabric, foam materials, metal, and any other appropriate type of material. A wide range of production techniques can be used: moulding, casting, thermoforming, vacuum forming, rolling sheet materials, welding, gluing, sewing, and any other appropriate method.

They can be manufactured in unfolded, folded, and partly or semi-folded states.

The foldable structures can be used not only for articles that are designed to be used multiple times but also for articles that are designed to be used just once, making their disposal, storage, packaging, and transportation more effective or even making them reusable.

The combinations of foldable modules described can be used not only for fully collapsible articles but also for parts and portions of articles. They can also combine with other appropriate folding patterns.

The cross sections of the cylindrical and conical modules are not required to be symmetrical curves. They can be asymmetrical and even have abrupt bends if these bends coincide with the internal edges/hinges in a module. They can also have straight sections. The main requirement is to have the appropriate circumferences for the particular sections. Their shape can also vary along the tube if the required length of the sections does not change significantly and the resulting surface is developable or a close enough approximation of a developable surface.

The surface elements are not required to be fully developable surfaces. They can be deformed in order to have double curvature especially when more smooth shape is needed but not maximum contraction is required. They can also be divided by adding extra edges/hinges if needed.

Approximations of the shape of the surface elements and the edges/hinges are also acceptable, depending on the desired qualities of the article.

Some examples of collapsible containers designed by using combinations of the foldable modules presented are shown from FIG. 69 to FIG. 78. Examples of foldable pipe structures are shown in FIG. 79 and FIG. 80.

Alternative applications are also possible. Foldable structures composed of the described modules can be used as pumps, syringes, and cookie presses. The fact that they are interactive and can provide different shapes in folded and partly folded states makes them appropriate for toys and modular construction games. Foldable coverage or insulation for pipes and containers can also be an alternative application. Other applications can be packaging, funnels, straws, dust and powder puffers, inflatable structures, bags, clothes, lampshades, collapsible furniture and shelter structures and parts for them. Different applications can be even combined in one task unification article. Even the qualities of objects made of rigid and solid materials are possible if a closed unfolded shell is filled with a fluid or a powder-like substance in order to block the folding process which can make it appropriate for handles, sticks, rolling pins and other appropriate articles. 

What is claimed is:
 1. An article or portion of an article comprising at least two foldably interconnected foldable sections where the said sections mutually hinder either their folding or unfolding during normal operation until additional force is applied on particular spots along the mutual foldable edges that connect the said sections, whereby the said article or the said portion of an article not only can perform almost as well as non-folding equivalents but also can have the advantages that foldability offers. 